Asymptotic behavior of a selfinteracting random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 126-132
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We consider a simple one-dimensional random walk with the statistical weight of each sample path given by $\pi_t(\omega)=\exp\{-\beta\sum_{0\leq i$, where $\beta$ has the meaning of negative temperature, and $V$ is a nonnegative decreasing function with finite support. We show that for $\beta>\beta_0$ the distribution of $\omega_n$ is concentrated in the area $\{|\omega_n|>c\,n\}$, where $c=c(\beta)>0$, and for $\beta0$ every sample path becomes localized, in the sense that $\omega_n$ never leaves some fixed interval.
Keywords:
potential, random walk, self-repulsive random walk, asymptotic behavior.
@article{TVP_2006_51_1_a8,
author = {S. A. Nadtochii},
title = {Asymptotic behavior of a selfinteracting random walk},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {126--132},
publisher = {mathdoc},
volume = {51},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a8/}
}
S. A. Nadtochii. Asymptotic behavior of a selfinteracting random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 126-132. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a8/